Hamza Yalcin's arrest comes as alarm grows over press freedom in Turkey, with dozens of journalists detained and foreign reporters also caught up in a crackdown under the state of emergency imposed after last year's coup attempt.
Yalcin, who lives in Sweden and has dual Swedish-Turkish citizenship, was arrested on August 3rd at Barcelona's El Prat airport and is being held while a Spanish court decides whether to extradite him or not.
According to Turkey's state-run Anadolu news agency, Yalcin, who writes for Odak, a left-wing online magazine critical of the government in Ankara, is wanted to appear in court in two separate cases.
The first it says relates to insulting Erdogan in his writings.
The second relates to making "propaganda" for an unspecified "terror group", which other media outlets have identified as the extreme left Revolutionary People's Liberation Party, also designated a "terrorist organization" by the United States and European Union.
But media rights campaign group Reporters Without Borders (RSF) says the warrant is an attempt "to try to silence criticism of the Turkish regime".
On Friday, Baltasar Garzon, a former judge who now defends WikiLeaks founder Julian Assange among others, called for his release.
"It's unacceptable to even consider that Spain could hand over the writer Yalcin to a regime that is raising serious doubts over its respect for human rights," he said in a statement.
Garzon joined a chorus of concern both from Spain and abroad.
Earlier this week, Barcelona's acting mayor Jaume Asens sent a letter to Spain's attorney general and to Turkey's ambassador raising the city hall's concerns.
Turkey ranks 155 on the latest RSF world press freedom index, below Belarus and the Democratic Republic of Congo, after dropping four places from its 2016 ranking.
Yalcin's arrest has been criticized by RSF as an attempt by Erdogan "to extend his power beyond the country's borders".
The International Federation of Journalists has also joined calls to release Yalcin, as has Spain's far-left opposition party Podemos.